Winner of the Wolf Prize for his contribution to our understanding of the universe, Penrose takes on the question of whether artificial intelligence will ever ...

A model of the neuropsychology of anxiety is proposed. The model is based in the first instance upon an analysis of the behavioural effects of the antianxiety drugs in animals. From such psychopharmacologi-cal experiments the concept of a “behavioural inhibition system” has been developed. This system responds to novel stimuli or to those associated with punishment or nonreward by inhibiting ongoing behaviour and increasing arousal and attention to the environment. It is activity in the BIS that constitutes anxiety and that (...) is reduced by antianxiety drugs. The effects of the antianxiety drugs in the brain also suggest hypotheses concerning the neural substrate of anxiety. Although the benzodiazepines and barbiturates facilitate the effects of γ-aminobutyrate, this is insufficient to explain their highly specific behavioural effects. Because of similarities between the behavioural effects of certain lesions and those of the antianxiety drugs, it is proposed that these drugs reduce anxiety by impairing the functioning of a widespread neural system including the septo-hippocampal system, the Papez circuit, the prefrontal cortex, and ascending monoaminergic and cholinergic pathways which innervate these forebrain structures. Analysis of the functions of this system suggests that it acts as a comparator: it compares predicted to actual sensory events and activates the outputs of the BIS when there is a mismatch or when the predicted event is aversive. Suggestions are made as to the functions of particular pathways within this overall brain system. The resulting theory is applied to the symptoms and treatment of anxiety in man, its relations to depression, and the personality of individuals who are susceptible to anxiety or depression. (shrink)

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Here Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, he (...) maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism. (shrink)

The book explores philosophical issues such as idealism and free will and speculates on the relationship of consciousness to quantum mechanics.

The measurement problem of quantum theory is discussed, and the difficulty of trying to solve it within the confines of a local, Lorentz-invariant physics is emphasised. This leads to the obvious suggestion to seek a solution beyond physics, in particular, by introducing the concept of consciousness. The resulting dualistic model, in the natural form suggested by quantum theory, is shown to differ in several respects from the classical model of Descartes, and to suggest solutions to some of the long-standing problems (...) concerning the relation of consciousness to the physical world. (shrink)

The emperor's new mind (hereafter Emperor) is an attempt to put forward a scientific alternative to the viewpoint of according to which mental activity is merely the acting out of some algorithmic procedure. John Searle and other thinkers have likewise argued that mere calculation does not, of itself, evoke conscious mental attributes, such as understanding or intentionality, but they are still prepared to accept the action the brain, like that of any other physical object, could in principle be simulated by (...) a computer. In Emperor I go further than this and suggest that the outward manifestations ofconscious mental activity cannot even be properly simulated by calculation. To support this view, I use various arguments to show that the results of mathematical insight, in particular, do not seem to be obtained algorithmically. The main thrust ofthis work, however, is to present an overview ofthe present state of physical understanding and to show that an important gap exists at the point where, quantum and classical physics meet, as well as to speculate on how the conscious brain might be taking advantage ofwhatever new physics is needed to fill this gap to achieve its nonalgorithmic effects. (shrink)

Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis. In Part One, he applies Scott- Solovay's Boolean-valued models of set theory to analysis by means of complete Boolean algebras of projections. In Part Two, he develops classical analysis including complex analysis in Peano's arithmetic, showing that (...) any arithmetical theorem proved in analytic number theory is a theorem in Peano's arithmetic. In doing so, the author applies Gentzen's cut elimination theorem. Although the results of Part One may be regarded as straightforward consequences of the spectral theorem in function analysis, the use of Boolean- valued models makes explicit and precise analogies used by analysts to lift results from ordinary analysis to operators on a Hilbert space. Essentially expository in nature, Part Two yields a general method for showing that analytic proofs of theorems in number theory can be replaced by elementary proofs. Originally published in 1978. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)